Exponential attractors for a singularly perturbed Cahn‐Hilliard system

By Messoud A. Efendiev, Alain Miranville, Sergey Zelik. 2004

109 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/6d68440d7edce0854710439c0caec004b09e22d9

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Citations in the corpus

Asymptotic behavior of a Cahn-Hilliard equation with Wentzell boundary conditions and mass conservation (2008, background): “, [1, 5, 28, 29]) by proving theorems about wellposedness and existence of global and/or exponential attractors.”
The Cahn-Hilliard Equation with Logarithmic Potentials (2011, unknown): “, [19], [35], [63], [65], [74], [76], [80], [82], [84], [140], [153], [157], [174], [175], [176], [177], [178], [180], [195], [204] and [216] for Neumann (or periodic) boundary conditions and to [51], [96], [97], [102], [170], [187], [190] and [210] for dynamic boundary conditions.”
Exponential attractors and finite-dimensional reduction for non-autonomous dynamical systems* (2005, methodology): “Moreover, it was shown in [ 11 ] that, under natural assumptions, it is possible to construct a one-parametrical family of exponential attractors M", " ∈ [0,1], associated with the one-parametrical family of semigroups S" satisfying (0.5) uniformly with respect to ", such that”
A construction of a robust family of exponential attractors (2005, background): “In fact, in that case, the theorem is just a slight generalization of the abstract results contained in [4, 5, 10].”
Exponential attractors for the Cahn–Hilliard equation with dynamic boundary conditions (2005, methodology): “Reference [21]), we deduce that family (108) of exponential attractors satis es assumptions (1)–(4) of Theorem 3.”
Chapter 3 Attractors for Dissipative Partial Differential Equations in Bounded and Unbounded Domains (2008, methodology): “(d) As in [70], the exponential attractors M , > 0, constructed in [83] depend both on S and S0.”
ROBUST EXPONENTIAL ATTRACTORS FOR SINGULARLY PERTURBED PHASE-FIELD TYPE EQUATIONS (2002, unknown): “in the estimate for the symmetric distance between the exponential attractors of the perturbed and unperturbed problems, see [14], [15] and below).”
ASYMPTOTIC BEHAVIOR OF THE CAHN-HILLIARD-OONO EQUATION (2011, background): “To finish the proof, it suffices to prove that the mapping (t, x) 7→ Sǫ(t)x is Hölder continuous on [0, t1]×B, uniformly with respect to ǫ ∈ [0, ǫ0] (see [5] and [7]).”
A Cahn–Hilliard model in bounded domains with permeable walls (2006, background): “Different versions of Cahn-Hilliard models were studied extensively by many authors in [4, 5, 14, 16, 18] and the references cited there in.”